Now, when trying to install the BES Express 5.0.2, the installation constantly crashens, when I try to get past the MAPI-Preferences (see attachement). When I click on "Next", the installation crashes.

I had the same problem and it seems it was to do with Active Directory.
I resolved it by doing a dcpromo on the server.

The next issue I had after getting past that step was right at the end of the installation where the installer crashed on the 2nd last page (I think). Installer was trying to use the BESMgmt database that was created before doing a dcpromo. If this happens to you, just rename the database (on the screen before your attached screenshot) to something else. I made it BESMgmt2, and everything worked after that.

ZCS server FQDN or BES server FQDN?
With or without ":7071" at the end?

I've tried all I could think of (as well as "localhost") but nothing "works".

The "Check Name" button always answers "The setup application could not contact the Microsoft Exchange Server to check the name of the mailbox".
And bypassing the test (clicking on "Next") hangs the application (with no error message, obviously).

ZCS server FQDN or BES server FQDN?
With or without ":7071" at the end?

I've tried all I could think of (as well as "localhost") but nothing "works".

The "Check Name" button always answers "The setup application could not contact the Microsoft Exchange Server to check the name of the mailbox".
And bypassing the test (clicking on "Next") hangs the application (with no error message, obviously).

I forgot to mention, after I did a dcpromo, I re-ran the install as a different domain user. I got the hanging and crashing because the mail profiles were created as administrator, and not the new user.

Make sure you re-create the BlackBerryServer and BlackBerryServer_MailStoreProfile mail profiles if your are running as a different user.